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It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Free GPL: Also a computer algebra system through interface with Maxima: Fityk: Marcin Wojdyr 2002 1.3.1 19 December 2016: $115 (1.x binaries), Free (source code and 0.x binaries) GPL: interactive graphics, scriptable, specialized in curve fitting and peak fitting, 2D only FlexPro: Weisang GmbH n/a 1991 2019 (12.0.x) 2018 Not free (commercial ...
Krylov subspaces are used in algorithms for finding approximate solutions to high-dimensional linear algebra problems. [2] Many linear dynamical system tests in control theory, especially those related to controllability and observability, involve checking the rank of the Krylov subspace.
The number indicates the degree of oxidation of each element caused by molecular bonding. In ionic compounds, the oxidation numbers are the same as the element's ionic charge. Thus for KCl, potassium is assigned +1 and chlorine is assigned -1. [4] The complete set of rules for assigning oxidation numbers are discussed in the following sections.
Oxidation state is an important index to evaluate the charge distribution within molecules. [2] The most common definition of oxidation state was established by IUPAC, [3] which let the atom with higher electronegativity takes all the bonding electrons and calculated the difference between the number of electrons and protons around each atom to assign the oxidation states.
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
The original classical Marcus theory for outer sphere electron transfer reactions demonstrates the importance of the solvent and leads the way to the calculation of the Gibbs free energy of activation, using the polarization properties of the solvent, the size of the reactants, the transfer distance and the Gibbs free energy of the redox reaction.